Updated Report on the Optimal Number of Positions in the Non-U.S. and Global Portfolios

January 1, 2013

In September of 2008, McKinley Capital Management, LLC (“McKinley Capital”) produced a white paper containing an analysis of the trade-off between minimum position size, number of positions required, and performance in its non-U.S. portfolios (1). In that paper, McKinley Capital concluded that it should lower its position threshold (PTH) to 35 basis points and increase the stock count to a maximum of 95 positions from the then existing maximum of 60 positions. Thereafter, McKinley Capital implemented the lower PTH of 35 basis points. Most of McKinley Capital’s clients with non-U.S. mandates increased the maximum number of holdings to 75 positions, with several mandates being raised to 95 positions. The mandates with a higher maximum number of positions are MSCI Investable Market Index based mandates. In those cases, the lower skew of the index weights leads to a higher optimal position count.

The purpose of this update is to analyze and report on the issue of maximum number of positions. Specifically, McKinley Capital simulated the performance of a non-U.S. portfolio from the end of 1996 to the end of June 2012 using the McKinley Capital current MQ model. Transaction costs and constraints were assumed in the simulation in an attempt to produce results which were as close to real portfolio management conditions as possible. The conditions and costs imposed are listed at the bottom of Table 3. As is typical of McKinley Capital’s back test studies, no attempt was made to simulate the impact of a qualitative or fundamental overlay. In that the purpose of this update was to study position count rather than minimum position size, a minimum position size or PTH of 35 basis points was assumed. A 6% maximum tracking error was assumed for the purpose of the study2. The main variable in the simulation is the maximum number of positions allowed. Five separate simulations were conducted where the maximum stock count varied from 65 stocks to 95 stocks.

The results of the study are reported in Table 1. Though, in each subsequent test, the simulation program was allowed to choose additional stocks, once a 75 stock maximum was exceeded, the optimization program did not often use the entire flexibility. The maximum average number of stocks selected was 84 positions when the optimizer was given the ability to select up to 95 names. Of course, that is an average number. In some months, the optimizer selected close to the maximum number of positions. The annualized return, Sharpe ratio, and information ratio reached a maximum when up to 90 positions in the portfolio were allowed. On average, the optimizer formed portfolios with 82 stocks at that level.

1301 Updated-01 Tab1

See assumptions provided below Table 3. Source: ClariFI Optimizer, FactSet data, 09/12

In the first set of simulations a trading volume constraint was specified. In practice, the constraint is that a position will not be initiated if more than 3X daily trading volume was averaged over the prior twenty days. In fact, many of McKinley Capital’s positions have significantly less than 3X average daily trading volume. If McKinley Capital were to select stocks with, on average, greater liquidity, would the optimal number of positions change? Put another way, would McKinley Capital need more stocks to adequately diversify if choices were limited to a more liquid set of stocks?
Tables 2 and 3 reflect the results of these simulations. Table 2 evidences the results of a simulation when position size was limited to no more than 2X average daily trading volume (the “2X” Table and study). Table 3 evidences the results of a simulation when position size was limited to no more than 1X average daily trading volume (the “1X” Table and study).

1301 Updated-02 Tab2

1301 Updated-03 Tab3

 

Assumptions for the Non-U.S. Simulations
Universe: All stocks in the MSCI ACWxUS Index
Simulation Period: January 1997 to June 2012 Risk Setting: Specific/Systematic Risk Acceptance Parameter 0.3 and targeted TE 6%
Risk Model: APT Statistical Risk Model
Optimizer: Clarifi Optimizer
Turnover: 8% Monthly
Transaction Cost: 1.50% each way
Holdings: Max = 1X,2X, or 3X DolVol/AUM or benchmark + 2% whichever is lower; Min = 1X,2X, or 3X DolVol/AUM or benchmark – 2% whichever is lower
PTH: 0.35%
Country: Country exposure to be within benchmark +/-7.5
Sector: Sector exposure to be within benchmark +/-7.5
AUM: $1.5 billion assumed on 12/31/96 that grows to $7.77 billion by 06/30/2012
MCAP: The weighted average MCAP of the portfolio was floored at 50% of the weighted average MCAP of the benchmark

The results are similar to the results of the 3X study. The 2X study results indicate a maximum annualized return, Sharpe ratio, and information ratio when the optimizer was permitted to choose up to 90 positions. On average, the optimizer formed portfolios with 83 stocks when allowed to hold up to 90 positions. The 1X study results indicate a maximum annualized return, Sharpe ratio, and information ratio when the optimizer was allowed to choose up to 85 stocks. On average, the optimizer formed portfolios with 82 stocks. While the optimal number of positions were similar across the three sets of simulations, the annualized returns improved, on the margin, as we allowed less liquid stocks into the portfolio. This is not surprising, and is partly the reason that McKinley Capital seeks to position less liquid stocks into its portfolios as liquidity allows.
As a final study, the performance of a global portfolio using the 1X volume constraint was simulated. The results are reflected in Table 4. As with the non-U.S. portfolio simulation, the maximum annualized return, Sharpe ratio, and information ratio was obtained when the optimizer was permitted to choose up to 85 stocks. With that maximum, on average, the optimizer formed portfolios with 78 stocks.

1301 Updated-04 Tab4

Assumptions for the Global Simulation
Universe: All stocks in the MSCI ACW Index
Simulation Period: January 1997 to June 2012
Risk Setting: Specific\Systematic Risk Acceptance Parameter 0.4 and targeted TE 6%
Risk Model: APT Statistical Risk Model
Optimizer: Clarifi Optimizer
Turnover: 8% Monthly
Transaction Cost: 1.50% each way
Holdings: Max = 1X DolVol/AUM or benchmark + 2% which ever is lower; Min = 1X DolVol/AUM or benchmark – 2% whichever is lower
PTH: 0.35%
Country: Country exposure to be within benchmark +/-7.5
Sector: Sector exposure to be within benchmark +/-7.5
AUM: $1 billion assumed on 12/31/96 that grows to $2 billion by 06/30/2012
MCAP: The weighted average MCAP of the portfolio was floored at 50% of the weighted average MCAP of the benchmark

Based on the results of these simulations, McKinley Capital continues to conclude that limiting non-U.S. and global portfolios to 75 positions might produce slightly sub-optimal portfolio management decisions at all levels of constraint on liquidity. However, there is a second way to look at this data.  Regardless of the number of stocks allowed in a portfolio, simulated performance improves when McKinley Capital imposes fewer liquidity constraints.  For example, with a 95 stock nonU.S. portfolio, the simulated annualized excess return is 3.16% when we position stocks at up to 3 times average daily trading volume.  The simulated annualized excess return falls to 1.74% when we position stocks up to 1 time average daily trading volume, even when we allow a 95 stock count.  Positioning less liquid stocks would seem, based on simulated tests, to result in better performance.

With secular declines in trading volume, McKinley Capital is finding it more and more difficult to reach into the lower liquidity set of Index names.  For example, in 2007, the median name in the ACWXUSG Index by average daily trading volume traded about $24.2 million per day on exchange.  As reflected in Table 5, by the second half of 2012 the volume had declined to about $15 million per day.  The 75th percentile name in the ACWXUSG Index traded about $7 million per day in the second half of 2012.  The chart below reflects a similar trend.

1301 Updated-05 Average

While trade size varies, a typical position for the McKinley Capital non-U.S. mandates with a 75 stock maximum is $25 million. Limiting McKinley Capital’s position to three times average daily trading volume implies that the stock’s average daily trading volume would have to average over $8 million to be considered for investment. While that would not have been much of an issue in 2007 and 2008, currently, McKinley Capital is not able to position stocks in the lowest and even the second lowest liquidity quartiles. If McKinley Capital allowed up to 95 positions, its typical position size would decline to about $19 million. Limiting McKinley Capital’s position to three times average daily trading volume implies that the stock’s average daily trading volume would then have to average slightly over approximately $6.3 million to be considered for investment. This enhancement would allow McKinley Capital to invest in some stocks in the lowest quartile of liquidity and all stocks in the higher quartiles, and allows significant investments in even the lowest market capitalization category. In summary, it appears that McKinley Capital could potentially enhance performance by increasing the maximum allowed number of positions in its non-U.S. and global accounts and by making full use of that increased flexibility. Therefore, McKinley Capital will implement this enhancement for those clients who already allow for more positions and for those who approve the proposed flexibility.

1301 Updated-06 Tab5

 

Disclaimer
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